Disease-causing microbes that have become resistant to drug therapy are an increasing public health problem. Tuberculosis, malaria, and ear infections are just a few examples of the diseases that have become difficult to treat with traditional antibiotic drugs. The recent discovery of a bacterial cytoskeleton with shape-defining function provides new molecular targets for anti-bacterial treatments. Indeed, cumulating results now suggest that bacteria contain proteins that are similar to actin and tubulin, although no cytoskeletal motor protein analogs have been found. A primary function of the prokaryotic cytoskeleton is in cell division (cytokinesis). In particular, the prokaryotic protein FtsZ is the major component of the division ring (Z-ring). The ring is dynamically maintained. At the end of the division cycle, the ring contracts to separate the cell into daughter cells. Using a computational approach validated by experiments, we address 3 central questions in Z-ring dynamics: 1) How does the Z-ring form in vivo? 2) How much force is needed to constrict E. coli cells at mid-point? 3) What is the mechanism of Z-ring contraction and how does it generate force without molecular motors? To answer these questions, we propose quantitative models that combine the elastic properties of the FtsZ filaments with the hydrolysis chemistry of FtsZ. The models require input parameters which are obtained from in vivo living-cell measurements. Quantitative theoretical models of the Z-ring assembly and dynamics will be directly tested experimentally. Z-ring contraction is a common division mechanism found in most bacteria. The revealed contraction mechanism could lead to the development of novel antibiotic drugs that target the division cycle of pathogenic bacteria.